// Copyright (C) 2025 Category Labs, Inc.
//
// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program.  If not, see <http://www.gnu.org/licenses/>.

use crate::binary_search::smallest_integer_satisfying;

#[derive(Debug)]
pub struct CodeParameters {
    num_source_symbols: u16,             // K in the RFC
    num_ldpc_symbols: u16,               // S in the RFC
    num_half_symbols: u8,                // H in the RFC
    num_intermediate_symbols: u16,       // L in the RFC
    num_intermediate_symbols_prime: u16, // L' in the RFC
    systematic_index: u16,               // J(K) in the RFC
}

// RFC 5053 section 5.2 suggests a minimum value of 4.
// RFC 5053 section 5.7 provides systematic indices for values of 4 and higher.
// We provide our own systematic indices for values of 1, 2, and 3.
pub const SOURCE_SYMBOLS_MIN: usize = 1;

// RFC 5053 section 5.1.2 defines Kmax to be 8192.
pub const SOURCE_SYMBOLS_MAX: usize = 8192;

const SMALL_PRIMES: [u16; 1052] = [
    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
    101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193,
    197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307,
    311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421,
    431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547,
    557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
    661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797,
    809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929,
    937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039,
    1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153,
    1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279,
    1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409,
    1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499,
    1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613,
    1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741,
    1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873,
    1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999,
    2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113,
    2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251,
    2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371,
    2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477,
    2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647,
    2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731,
    2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857,
    2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001,
    3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163,
    3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299,
    3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407,
    3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539,
    3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659,
    3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793,
    3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919,
    3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051,
    4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201,
    4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327,
    4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463,
    4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603,
    4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733,
    4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903,
    4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009,
    5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153,
    5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303,
    5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441,
    5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569,
    5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701,
    5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843,
    5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987,
    6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131,
    6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269,
    6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373,
    6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553,
    6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691,
    6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829,
    6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967,
    6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109,
    7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247,
    7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451,
    7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559,
    7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687,
    7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841,
    7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993,
    8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147,
    8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287,
    8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419,
];

// The code parameters are computed from the source symbol count according to the
// procedure described in RFC 5053 section 5.4.2.3.
impl CodeParameters {
    // "Let X be the smallest positive integer such that X*(X-1) >= 2*K"
    // where X = x, K = num_source_symbols.
    //
    // For num_source_symbols in [4, 8192], the lower bound for x is 4:
    // - For x = 3,   x*(x-1) = 6      < 2*4.
    // - For x = 4,   x*(x-1) = 12    >= 2*4.
    //
    // For num_source_symbols in [4, 8192], the upper bound for x is 129:
    // - For x = 128, x*(x-1) = 16256  < 2*8192.
    // - For x = 129, x*(x-1) = 16512 >= 2*8192.
    const X_MIN: usize = 4;
    const X_MAX: usize = 129;

    fn determine_x(num_source_symbols: u16) -> Result<u8, String> {
        match smallest_integer_satisfying(Self::X_MIN, Self::X_MAX + 1, |pivot| {
            pivot * (pivot - 1) >= (2 * num_source_symbols).into()
        }) {
            None => Err(format!(
                "Can't find x for num_source_symbols = {}",
                num_source_symbols
            )),
            Some(x) => Ok(u8::try_from(x).unwrap()),
        }
    }

    fn smallest_prime_greater_or_equal(prime_min: u16) -> Result<u16, String> {
        match smallest_integer_satisfying(0, SMALL_PRIMES.len(), |pivot| {
            SMALL_PRIMES[pivot] >= prime_min
        }) {
            None => Err(format!("Can't find small prime >= {}", prime_min)),
            Some(index) => Ok(SMALL_PRIMES[index]),
        }
    }

    fn determine_num_ldpc_symbols(num_source_symbols: u16, x: u8) -> Result<u16, String> {
        // "Let S be the smallest prime integer such that S >= ceil(0.01*K) + X"
        // where S = num_ldpc_symbols, K = num_source_symbols.
        let num_ldpc_symbols_min = ((num_source_symbols + 99) / 100) + u16::from(x);

        // For num_source_symbols = 4, X = 4, and so, num_ldpc_symbols >= 1 + 4 = 5.
        // For num_source_symbols = 8192, X = 129, and so, num_ldpc_symbols >= 82 + 129 = 211.
        Self::smallest_prime_greater_or_equal(num_ldpc_symbols_min).map_err(|_| {
            format!(
                "Can't find num_ldpc_symbols for num_source_symbols = {}, X = {}",
                num_source_symbols, x
            )
        })
    }

    fn choose(n: u8, k: u8) -> u16 {
        // For H = 16, H! / (H - H/2)! = 518918400, which fits into 32 bits.
        let mut choose: u32 = 1;

        // Compute n! / k!.
        for val in k + 1..=n {
            choose *= u32::from(val);
        }

        // Divide by (n - k)!.
        for val in 2..=n - k {
            choose /= u32::from(val);
        }

        // For H = 16, choose(H, H/2) = 12870, which fits into 16 bits.
        choose.try_into().unwrap()
    }

    // "Let H be the smallest integer such that choose(H,ceil(H/2)) >= K + S"
    // where H = num_half_symbols, K = num_source_symbols, S = num_ldpc_symbols.
    //
    // The lower bound for num_half_symbols is 5, as for num_source_symbols = 4,
    // num_ldpc_symbols = 5, and so, num_source_symbols + num_ldpc_symbols = 9, and:
    // - choose(4, 2) = 6.
    // - choose(5, 3) = 10.
    //
    // The upper bound for num_half_symbols is 16, as for num_source_symbols = 8192,
    // num_ldpc_symbols = 211, and so, num_source_symbols + num_ldpc_symbols = 8403, and:
    // - choose(15, 8) = 6435.
    // - choose(16, 8) = 12870.
    const HALF_MIN: usize = 5;
    const HALF_MAX: usize = 16;

    fn determine_num_half_symbols(
        num_source_symbols: u16,
        num_ldpc_symbols: u16,
    ) -> Result<u8, String> {
        let num_half_symbols =
            smallest_integer_satisfying(Self::HALF_MIN, Self::HALF_MAX + 1, |pivot| {
                let pivot = pivot.try_into().unwrap();

                Self::choose(pivot, (pivot + 1) / 2) >= num_source_symbols + num_ldpc_symbols
            });

        match num_half_symbols {
            None => Err(format!(
                "Can't find num_half_symbols for num_source_symbols = {}, num_ldpc_symbols = {}",
                num_source_symbols, num_ldpc_symbols
            )),
            Some(num_half_symbols) => Ok(num_half_symbols.try_into().unwrap()),
        }
    }

    pub fn new(num_source_symbols: usize) -> Result<CodeParameters, String> {
        if !(SOURCE_SYMBOLS_MIN..=SOURCE_SYMBOLS_MAX).contains(&num_source_symbols) {
            return Err(format!(
                "num_source_symbols {} not in range {}..{}",
                num_source_symbols, SOURCE_SYMBOLS_MIN, SOURCE_SYMBOLS_MAX
            ));
        }

        let num_source_symbols: u16 = num_source_symbols
            .try_into()
            .map_err(|err| format!("{}", err))?;
        let x = Self::determine_x(num_source_symbols)?;
        let num_ldpc_symbols = Self::determine_num_ldpc_symbols(num_source_symbols, x)?;
        let num_half_symbols =
            Self::determine_num_half_symbols(num_source_symbols, num_ldpc_symbols)?;
        let num_intermediate_symbols =
            num_source_symbols + num_ldpc_symbols + u16::from(num_half_symbols);
        let num_intermediate_symbols_prime =
            Self::smallest_prime_greater_or_equal(num_intermediate_symbols)?;
        let systematic_index = Self::determine_systematic_index(num_source_symbols)?;

        Ok(CodeParameters {
            num_source_symbols,
            num_ldpc_symbols,
            num_half_symbols,
            num_intermediate_symbols,
            num_intermediate_symbols_prime,
            systematic_index,
        })
    }

    pub fn num_source_symbols(&self) -> usize {
        self.num_source_symbols.into()
    }

    pub fn num_ldpc_symbols(&self) -> usize {
        self.num_ldpc_symbols.into()
    }

    pub fn num_half_symbols(&self) -> usize {
        self.num_half_symbols.into()
    }

    pub fn num_intermediate_symbols(&self) -> usize {
        self.num_intermediate_symbols.into()
    }

    pub fn num_intermediate_symbols_prime(&self) -> usize {
        self.num_intermediate_symbols_prime.into()
    }

    pub fn systematic_index(&self) -> usize {
        self.systematic_index.into()
    }
}

#[cfg(test)]
mod test {
    use super::{CodeParameters, SMALL_PRIMES, SOURCE_SYMBOLS_MAX, SOURCE_SYMBOLS_MIN};

    fn determine_x_slow(num_source_symbols: u16) -> Result<u8, ()> {
        for x in CodeParameters::X_MIN..=CodeParameters::X_MAX {
            if x * (x - 1) >= (2 * num_source_symbols).into() {
                return Ok(u8::try_from(x).unwrap());
            }
        }

        Err(())
    }

    #[test]
    fn test_x() {
        for num_source_symbols in 0..=u16::try_from(SOURCE_SYMBOLS_MAX + 100).unwrap() {
            assert_eq!(
                CodeParameters::determine_x(num_source_symbols).map_err(|_| ()),
                determine_x_slow(num_source_symbols).map_err(|_| ())
            );
        }
    }

    fn smallest_prime_greater_or_equal_slow(prime_min: u16) -> Result<u16, ()> {
        for prime in SMALL_PRIMES {
            if prime >= prime_min {
                return Ok(prime);
            }
        }

        Err(())
    }

    #[test]
    fn test_prime() {
        for prime_min in 0..=10000 {
            assert_eq!(
                CodeParameters::smallest_prime_greater_or_equal(prime_min).map_err(|_| ()),
                smallest_prime_greater_or_equal_slow(prime_min).map_err(|_| ())
            );
        }
    }

    fn determine_num_half_symbols_slow(
        num_source_symbols: u16,
        num_ldpc_symbols: u16,
    ) -> Result<u8, ()> {
        for num_half_symbols in CodeParameters::HALF_MIN..=CodeParameters::HALF_MAX {
            let num_half_symbols = u8::try_from(num_half_symbols).unwrap();

            if CodeParameters::choose(num_half_symbols, num_half_symbols.div_ceil(2))
                >= num_source_symbols + num_ldpc_symbols
            {
                return Ok(num_half_symbols);
            }
        }

        Err(())
    }

    #[test]
    fn test_half() {
        for num_source_symbols in SOURCE_SYMBOLS_MIN..SOURCE_SYMBOLS_MAX {
            let num_source_symbols = u16::try_from(num_source_symbols).unwrap();
            let x = CodeParameters::determine_x(num_source_symbols).unwrap();
            let num_ldpc_symbols =
                CodeParameters::determine_num_ldpc_symbols(num_source_symbols, x).unwrap();

            assert_eq!(
                CodeParameters::determine_num_half_symbols(num_source_symbols, num_ldpc_symbols)
                    .map_err(|_| ()),
                determine_num_half_symbols_slow(num_source_symbols, num_ldpc_symbols)
                    .map_err(|_| ())
            );
        }
    }
}
